Respuesta :
It is 4 times as tall.
Let h₁ be the height of the box with the smaller base and h₂ be the height of the box with the larger base.
The volume of the box with the smaller base is given by 2(2)(h₁). The volume of the box with the larger base is given by 4(4)(h₂). Since they are equal:
2(2)(h₁)=4(4)(h₂)
4h₁=16h₂
Dividing both sides by 4,
4h₁/4 = 16h₂/4
h₁ = 4h₂
The height of the box with the smaller base is 4 times the height of the box with the larger base.
Let h₁ be the height of the box with the smaller base and h₂ be the height of the box with the larger base.
The volume of the box with the smaller base is given by 2(2)(h₁). The volume of the box with the larger base is given by 4(4)(h₂). Since they are equal:
2(2)(h₁)=4(4)(h₂)
4h₁=16h₂
Dividing both sides by 4,
4h₁/4 = 16h₂/4
h₁ = 4h₂
The height of the box with the smaller base is 4 times the height of the box with the larger base.
Volume is a three-dimensional scalar quantity. The base of the smaller box is 4 times taller than the base of the bigger base.
What is volume?
A volume is a scalar number that expresses the amount of three-dimensional space enclosed by a closed surface.
The volume of a box is the product of its base and its height. Now, since it is given that the volume of the two boxes is the same. Therefore, we can write,
[tex]\rm (\text{Volume of Box})_1 = (\text{Volume of Box})_2\\\\(\text{Area of the base})_1 \times Hieght_1=(\text{Area of the base})_2 \times Hieght_2\\[/tex]
Given the base of box 1 is 2 inches by 2 inches, while the base of box 2 is 4 inches by 4 inches.
[tex]\rm (\text{Area of the base})_1 \times Height_1=(\text{Area of the base})_2 \times Height_2\\\\(2 \times 2) \times (Height_1)=(4 \times 4) \times (Height_2)\\\\4(Height_1) = 16(Height_2)\\\\4(Height_1) = \dfrac{16(Height_2)}{4}\\\\4(Height_1) = 4(Height_2)[/tex]
Hence, the base of the smaller box is 4 times taller than the base of the bigger base.
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